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Branching problems for representations of reductive Lie groups

Clemens Weiske (Aarhus University)
Wednesday, 25 November, 2020, at 15:00-16:00, The talk will be given on Zoom. Please, contact the organizers for more information.

Let G be a group and H be a subgroup of G. The restriction of a representation of G to H automatically defines a representation of the subgroup and describing the restriction is called a branching problem. For irreducible representations of finite and compact Lie groups this problem is completely solved and every irreducible representation of G decomposes as a direct sum of irreducible representations of H. For more general groups, for example reductive Lie groups, irreducible representations are typically infinite dimensional and there is no direct sum decomposition anymore. In this case these problems are far from solved and have gained some attention recently. I will try to give an overview of problems and technics concerning branching problems for certain smooth or unitary representations of reductive Lie groups and show examples.

Organised by: Seminar of the Young Mathematicians of Aarhus
Contact person: Benjamin Alvarez and Polyxeni Spilioti